A knight defends against a passed pawn by controlling the square in front of it and jumping with check whenever the enemy king attacks it. The knight's checks keep it alive and on the critical squares.
A lone knight can hold a lone pawn as long as it reaches the squares around the promotion square in time and does not get trapped. The pawn on d3 wants d2 and d1; the knight on f1 must guard d2 right now.